The present invention relates generally to integrators, and more specifically to an integrator with a long time constant.
The integrator is a key building block for analog signal processing. It attenuates high-frequency signals, shapes low-frequency signals, and tracks DC levels.
FIG. 1 shows a conventional operational amplifier integrator. The resistor (R) converts the input voltage vin to a current that can be expressed as:       i          i      ⁢              xe2x80x83            ⁢      n        =                    v                  i          ⁢                      xe2x80x83                    ⁢          n                    -              V                  (          -          )                      R  
where V(xe2x88x92) is the voltage at the inverting terminal of the operational amplifier. The operational amplifier""s large gain forces the voltages at its input terminals V(xe2x88x92) and V(+) to be equal, while its high input impedance directs the input current iin to the capacitor. This causes a voltage to be developed across the capacitor (C) given by:                     v        c            =                        1          C                ⁢                  ∫                                    i                              i                ⁢                                  xe2x80x83                                ⁢                n                                      ⁢                          ⅆ              t                                            ⁢          xe2x80x83            with    ;              v      out        =                  -                  v          C                    =                        1          RC                ⁢                  ∫                                    v                              i                ⁢                                  xe2x80x83                                ⁢                n                                      ⁢                          ⅆ              t                                          
where RC is the time constant of the integrator.
A typical integrator uses large-valued resistors and capacitors to realize a long time constant, making it difficult to implement in monolithic form. As a result, off-chip capacitors are used or shorter time constants with some compromise are substituted.
The above integrator operates continuously as opposed to the switched-capacitor integrator shown in FIG. 2. The switched-capacitor integrator is a discrete-time circuit that is capable of long time constants. During operation, when the switch is connected to the input, the input voltage vin charges capacitor C1. The charge QC1 stored by the capacitor C1 is simply equal to:
QC1=C1vin
When the switch is connected to the inverting input of the operational amplifier, the capacitor C1 is discharged to ground through capacitor C2. (Since the large gain of the operational amplifier drives its inverting terminal to be equal to its noninverting terminal.) That is, for each cycle of the switch, a packet of charge is transferred from the input to the integrating capacitor C2. The equivalent input current is therefore equal to:
Ieq=QC1fs=C1fsvin
where fs is the switching frequency. This results in an equivalent resistance (Req) of:       R    eq    =                    v                  i          ⁢                      xe2x80x83                    ⁢          n                            I        eq              =          1                        C          1                ⁢                  f          s                    
As with any discrete-time system, the switching frequency must be several times higher than the highest input frequency. However, by their nature, switched capacitor circuits generate switching noise that can affect other circuits and produce discrete-time outputs that typically require filtering to smooth the steps between discrete values.
It would therefore be advantageous to have a continuous-time integrator using nominal-valued components to achieve a long time constant.
The present invention includes a differential integrator circuit that uses a resistor array to reduce integrating current and thereby realize a long time constant. The performance of the circuit is based on resistor matchingxe2x80x94a strong property in monolithic circuitsxe2x80x94and nominal-valued components to achieve the long time constant.
In one embodiment of the invention, a long time-constant differential integrator is provided that comprises a differential operational amplifier having inverting and noninverting amplifier input terminals, and inverting and noninverting amplifier output terminals, and the output terminals form inverting and noninverting output terminals, respectively, of the differential integrator. The differential integrator also comprises a noninverting differential integrator input terminal and an inverting differential integrator input terminal. The differential integrator also comprises a resistor array that couples the noninverting differential integrator input terminal to the inverting and noninverting input terminals of the amplifier, and the resistor array also couples the inverting differential integrator input terminal to the inverting and noninverting input terminals of the amplifier.
In one embodiment, a long time-constant differential integrator is provided that comprises a differential operational amplifier having inverting and noninverting amplifier input terminals, and inverting and noninverting amplifier output terminals, and wherein the amplifier output terminals form inverting and noninverting output terminals, respectively, of the differential integrator. The differential integrator also comprises a noninverting differential integrator input terminal and an inverting differential integrator input terminal. The differential integrator also comprises a resistor array that couples the noninverting differential integrator input terminal to the inverting and noninverting input terminals of the amplifier, and the resistor array also couples the inverting differential integrator input terminal to the inverting and noninverting input terminals of the amplifier.